Methodology using odd harmonic components of an induced magnetic field for analyzing superconducting magnetic materials and their properties

ABSTRACT

An improved AC susceptometer and methodology for its use which is particularly suitable for the characterization of the properties of superconducting materials. Added to the circuitry of a conventional AC susceptometer is frequency domain analytical equipment for measuring the induced magnetic response. The addition of frequency domain measuring equipment permits the determination of the harmonic components of the induced magnetic response. The measurement of the harmonic components of the response also provides novel methodology for studying the phenomena of flux penetration, flux pinning and movement and permits the measurement of parameters such as lower critical field, critical temperatures, and the irreversibility line.

This is a continuation of application Ser. No. 07/455,730, filed Dec.21, 1989, now abandoned, which is a divisional of application Ser. No.07/416,286 filed Oct. 2, 1989, now abandoned.

BACKGROUND OF THE INVENTION

This application is directed to an improved AC susceptometer formeasuring the properties of magnetic materials. This application is alsodirected to methodology for measuring the magnetic properties ofmaterials.

AC susceptometers are widely used in measuring magnetic properties ofmagnetic materials in general and of superconducting materials inparticular. The basic circuit of these systems is described in FIG. 1.It consists of a primary coil 20 coaxial with a pair of balanced coils22,24, one of which, 24 contains the sample to be measured. A sinusoidalmagnetic filed of a given frequency is created by the current output ofan oscillator 26 energizing primary coil 20. This alternating fieldinduces oscillations in the magnetization of the material, and as aresult an off-balance voltage is induced in the coil pair. Thematerial's response is measured by monitoring this signal at the drivingfrequency using a two-phase lock-in amplifier 28. The in-phase and theπ/2 out-of-phase signals are used to derive the real part (χ') andimaginary part (χ") of the magnetic susceptibility of the material. Inthe case of materials such as superconductors, required to be maintainedat a certain temperature, a cryostat 30 surrounds the coils 20, 22, 24.

This measurement technique is well suited for the characterization ofmaterial with a linear magnetic behavior, i.e., materials in which apure sinusoidal field induces pure sinusoidal oscillations in themagnetization at the same frequency. However, under certain temperatureand bias field conditions, materials can exhibit a nonlinear magneticbehavior; namely, a pure sinusoidal field can induce nonsinusoidaloscillations in the magnetization. Thus a nonsinusoidal voltage isinduced across the sample coil and components of the voltage atharmonics of the driving frequency are generated. Conventional ACsusceptometers measure the response of the material at the drivingfrequency, ignoring the harmonic components of the response.

In a previous application, of which we are coinventors entitled"Non-Contact Test of Materials for Superconductivity" Ser. No. 380,162now U.S. Pat. No. 5,004,726, filed Jul. 14, 1989 a simple device fordetecting superconductive transitions was described.

SUMMARY OF THE INVENTION

In this application we describe an improved system which measures thealternating magnetic response of the sample material at the drivingfrequency as well as at harmonics of this frequency. New techniques formeasuring the properties of magnetic materials are also disclosed. Thisimproved system enables the characterization of nonlinear magneticproperties of materials. In the special case of superconductingmaterials, the new system provides a tool for studying the phenomena offlux penetration, flux pinning and movement in these materials.Specifically, it enables the measurements of additional parameters ofpractical and fundamental importance such as the lower critical fieldand the irreversibility line.

The known AC susceptometers are improved by the addition of frequencydomain analysis of the output signal. Frequency domain analysis of theharmonics, as well as the fundamental frequency, permits measurementswhich were either not possible or difficult with time domain analysis.Additionally, the improved AC susceptometer permits analyticalmethodology which is distinct from that previously utilized.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the invention, reference is made to thefollowing drawings, which are to be taken in conjunction with thedetailed specification to follow, in which:

FIG. 1 is a schematic diagram of the conventional AC susceptometerutilized to measure the magnetic response of materials;

FIG. 2 is a schematic diagram of the improved AC susceptometer whichpermits improved analytical methodology;

FIG. 3 is a frequency domain plot of the fundamental and harmonics ofthe output signal from the AC susceptometer for a sample ofsuperconducting material at temperatures below and in the vicinity ofits critical temperature;

FIG. 4 is a plot of the third harmonic signal versus temperature of asample of superconducting material cooled below its transition point;

FIG. 5 is, on the bottom, a plot of the third harmonic signal of amultiphase sample of superconducting material with, on the top, a plotof its magnetic susceptibility;

FIG. 6 is a plot of third harmonic signal versus magnetic fieldstrength, illustrating the methodology utilized to calculate lowercritical field;

FIG. 7 is a third harmonic signal versus temperature plot of a sample ofsuperconducting material at various magnetic field strengths utilized inthe calculation of the irreversibility line; and

FIG. 8 is a temperature versus magnetic field strength graph showing theirreversibility line plotted thereon.

DETAILED DESCRIPTION OF THE DRAWING

A block diagram of the improved system is shown in FIG. 2. The coilsystem 20, 22, 24 is the same as in the conventional AC susceptometer,as described above with respect to FIG. 1. The output of the balancedpick-up coils 22, 24 is provided to a lock-in amplifier 28 that measuresthe phase content of the difference signal at the driving frequency. Asecond output is provided to a spectrum analyzer 36 through an amplifier34 to allow frequency domain measurement of the harmonics of the outputsignal. A scanner 38, temperature sensor 42 and a computer 40 areincluded in the system to permit simultaneous measurement of the inphase and out-of-phase signals as well as the amplitude of the harmoniccomponents as a function of temperature and external bias fields.Optionally a plotter 44 and a digital voltmeter 46 may be included inthe system to facilitate data measurement and display. An IEEE-488 busis a preferable means of connecting the various components in order toenable computer 40 to sequence and control the various measurements.This system is distinguished from the conventional systems by itsability to measure the frequency spectrum of the magnetic response ofmaterials to alternating fields. The following examples show theusefulness of such measurements in the characterization ofsuperconducting materials.

A) Determination of superconducting transitions

Type II superconductors exhibit a nonlinear magnetic behavior in a closevicinity of the transition temperature. T_(c). Above the transitiontemperature, and far below this point, the magnetic behavior is linear.Thus, the superconducting transition is accompanied by the generation ofharmonic components in the spectrum of the material's response to asinusoidal field. This phenomenon is demonstrated in FIG. 3. The tracesin this figure show the power spectra of the magnetic response of asintered Y-Ba-Cu-O superconductor (T_(c) ≈89K) to a sinusoidal field ofamplitude 0.04 Oe and frequency 20 kHz. The upper trace describes thespectrum of the response at 77K. It shows only the fundamental component(point A of the upper plot) at the driving frequency (20 kHz),indicating a linear magnetic response. The lower trace in FIG. 3describes the spectrum at 88K. This spectrum contains additionalcomponents (points B, C, D and E) at odd harmonics (third, fifth,seventh and ninth) of the driving frequency, indicating a nonlinearmagnetic behavior. Measurement of the amplitude of the third harmoniccomponent as a function of temperature (see FIG. 4) shows a peak (pointF) near the transition temperature. However transition temperature ismore accurately determined by the onset (point G) of the third harmonicsignal as the material transforms into the superconducting phase.

FIG. 5 describes the magnetic behavior of a multiphase sample (i.e. asample that has both non-superconducting and superconducting regions).The upper curve describes the temperature dependence of magneticsusceptibility which indicates a transition near 91K (point I). However,a close examination of this data reveals traces of additionaltransitions near 79K (point K) and 87K (point J). These transitions areclearly demonstrated in the measurement of the third harmonic signal aslarge peaks (lower curve of FIG. 5 points I', J', K'). Thus, frequencydomain analysis greatly improves the determination of the multiplesuperconducting transistions in multiphase samples.

B) Measurement of the lower critical field

The lower critical field, H_(c1) is usually determined from DCmeasurements of the magnetization curve. The onset of nonlinear behaviorin the magnetization versus field curve is identified as H_(c1). Theaccuracy of this method is limited because of the difficulty indetecting relatively small deviations from linearity just above H_(c1).Measurements of harmonic components in the alternating magnetic responseprovides a new tool for more accurate determination of H_(c1). In orderto probe H_(c1), at a given temperature, a sinusoidal field issuperimposed on a colinear steady bias field. As the steady bias fieldis incrementally raised, the onset of nonlinear behavior of themagnetization at H_(c1) is indicated by the appearance of harmoniccomponents in the response. This is illustrated in FIG. 6 whichdescribes a measurement of the amplitude of the third harmonic signal asa function of the bias field in a sintered sample of Y-Ba-Cu-O at 77K.The third harmonic signal remains below the background noise level asthe bias field is increased from 0 up to about 60 Oe, and rises abruptlythereafter. The critical field H_(c1) can be determined by extrapolatingthe roughly linear rise of the third harmonic signal downward to a zeronoise level. As is shown in FIG. 6 if one extends the linear portions ofeach component of the line the extensions cross at point L. The lowercritical field H_(C1) is thus seen to be located at 64 oersteds.

C) Measurement of the irreversibility line.

The temperature dependence of the lower and upper critical fields,H_(c1) and H_(c2), describe two lines in the field-temperature plane.Below the H_(c1) -line the material is in a superconducting state, i.e.magnetic flux is completely excluded from the interior of the material.Above this line and below the H_(c2) -line the material is in a mixedstate. In this state, flux penetrates the material in a form of smallflux tubes parallel to the field. The core of each tube is normal(nonsuperconducting), but the material surrounding each flux tuberemains superconducting. Above the H_(c2) -line the material is in thenormal state.

Recently, a new line was disclosed in the region between the H_(c1) andH_(c2) lines. This so called "irreversibility" line describes a linebelow which irreversibility in the magnetization sets in as a result offlux pinning. Above this line, thermal activation permits unpinning offlux lines within the time scale of the experiment.

It is practically important to determine the irreversibility linebecause high critical current density can be expected only below thisline. Using the improved AC susceptometer, one can determine theirreversibility line by measuring the temperature dependence of theharmonic components under steady bias fields. The transition from anonlinear, irreversible behavior of the magnetization below theirreversibility line to a linear, reversible behavior above this line isindicated by disappearance of the harmonic components.

FIG. 7 shows the results of measurements performed on a sinteredY-Ba-Cu-O sample at a number of magnetic field strengths. It is seenthat the third harmonic signal exhibits a sharp drop to the noise levelat well defined temperatures. See points M, N, O, P on FIG. 7. Thesetemperatures shift down as the bias field increases. In FIG. 8 points M,N, O, P are plotted as a function of temperature versus magnetic field.Measurement of these transition temperatures for different bias fieldsyields the irreversibility line as shown in FIG. 8 which is interpolatedthrough the plotted points.

The above examples show that the upgraded AC susceptometer, whichincludes provision for measuring the harmonic components of thealternating magnetic response, provides unique capabilities incharacterization of superconducting materials. Specifically, this systemis distinguished from conventional susceptometers by its ability tomeasure nonlinear magnetic properties. Although the present disclosurerefers the system described in FIG. 2, it is understood thatmodifications may be resorted to without departing from the basicconcept of the invention. For example, the spectrum analyzer in FIG. 2may be replaced by a low cost circuit for detection of the harmonicsignals. Such modifications are considered to be within the scope of theinvention.

What is claimed is:
 1. A method for measurement of lower critical fieldof a sample of superconductive material, comprising the steps of:coolingthe material to the temperature at which the lower critical field is tobe measured; applying a magnetic bias field to the sample of material;superimposing a sinusoidally varying field on said bias field; alteringthe strength of the bias field; measuring the amplitude of the oddnumbered harmonic component of the induced magnetic field in the sample;graphically displaying the amplitude of the odd numbered harmonic signalas a function of bias field strength, said amplitude generally appearingconstant at lower field strengths, which represents background noise,and a sloped line rising at a certain amplitude; and determining thelower critical field by interpolating the sloped line of the amplitudeof the odd numbered harmonic component with the background noise level.2. The method as claimed in claim 1 wherein the odd numbered harmoniccomponent comprises the third harmonic.
 3. A method for determining theirreversibility line of a sample of superconductive material comprisingthe steps of:cooling the sample of superconductive material; applying anumber of different bias fields to said sample of material; measuringthe amplitude of an odd numbered harmonic component of the magneticfield induced in the sample of material; displaying graphically theamplitude of the odd numbered harmonic component versus temperature atthe different bias field strengths; determining the temperature at whichthe odd numbered harmonic component exhibits a sharp drop to the noiselevel for each of the bias field strengths; and plotting thetemperatures at which the bias fields drop to the noise level as afunction of magnetic field strength, the line interpolated through thesetemperatures providing the irreversibility line.
 4. The method asclaimed in the claim 3 wherein the odd numbered harmonic component isthe third harmonic.